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The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics. This volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn. Contributions by Grégory Ginot, Thomas M. Fiore and Igor Kriz, Toshiro Hiranouchi and Satoshi Mochizuki, Paulo Carrillo Rouse, Donatella Iacono and Marco Manetti, John Terilla, Anne Pichereau - Researchers in the fields of deformation theory, noncommutative geometry, algebraic topology, mathematical physics - Advanced graduate students in mathematics Dr. Hossein Abbaspour, Department of Mathematics, Université de Nantes, France. Prof. Dr. Matilde Marcolli, Department of Mathematics, California Institute of Technology, Pasadena, California, USA. Dr. Thomas Tradler, Department of Mathematics, New York City College of Technology (CUNY), New York, USA.

Algebraic stacks. --- Homology theory. --- Moduli theory. --- Homology theory --- Algebraic stacks --- Moduli theory --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Geometry --- Theory of moduli --- Stacks, Algebraic --- Cohomology theory --- Contrahomology theory --- Mathematics. --- Algebra. --- Algebraic geometry. --- Geometry. --- Algebraic Geometry. --- Analytic spaces --- Functions of several complex variables --- Geometry, Algebraic --- Algebraic topology --- Geometry, algebraic. --- Mathematical analysis --- Euclid's Elements --- Algebraic geometry